Define force diagram .

A force diagram is a sketch of a situation showing every force acting on each particle, each drawn as an arrow pointing the way that force acts. The magnitude of each force is written beside its own arrow, in newtons.

Why must a force diagram often show forces that the question never mentions?

Because the diagram has to show every force acting on the particle, not only the ones the question happens to name. An object with mass always has a weight, and an object resting on a surface always has a normal reaction, so both belong on the diagram whether or not the question refers to them.

A block on a slope is connected over a pulley to a hanging mass. Besides the forces, what else should the diagram show?

The direction of the acceleration of each object, marked with its own arrow. The two arrows point different ways, since one object descends while the other rises, and marking them settles which direction counts as positive in each equation of motion.

True or False? On a force diagram for a block on a slope, the weight arrow is drawn perpendicular to the slope.

False. The weight acts vertically downwards whatever the surface is doing, so on a slope its arrow is not perpendicular to the plane. It is the normal reaction that is perpendicular to the slope, so the two arrows sit at an angle to each other rather than in line.

In a connected system, why must you be careful about which particle each force acts on?

Because an equation of motion describes one particle at a time, and it may contain only the forces acting on that particle. The tension in a connecting string acts on both, but the weight of one object acts on that object alone, so putting it into the other's equation would be wrong.

Define resultant force .

The resultant force is the sum of all the forces acting on a particle. It is the single force that would have exactly the same effect as all of those forces combined.

State Newton's first law of motion.

An object at rest stays at rest, and an object moving with constant velocity keeps moving with constant velocity, unless an unbalanced force acts on it . An unbalanced force is one that is not cancelled by another force in the opposite direction, so it leaves a resultant force that is not zero, and the object accelerates.

Define equilibrium , for a particle.

A particle is in equilibrium when the resultant force acting on it, the sum of all the forces, is zero . Every force is then cancelled by others, so the particle does not accelerate.

The resultant force on a particle is zero. What can you say about how it is moving?

The particle is either at rest or moving with constant velocity . A zero resultant force does not mean the particle is stationary. It means the particle is not accelerating, so whatever it was doing, it carries on doing.

Define coplanar forces .

Coplanar forces are forces that all lie in the same plane, so the whole situation can be drawn on one flat diagram. Working in two dimensions means working with coplanar forces.

What must be true of the two directions you resolve in?

They must be perpendicular to each other. A force lying along one of them then has no effect along the other, which is what lets the two directions be treated as two separate one-dimensional problems.

A particle in a plane has several forces acting on it. What has to be true in each of your two directions for it to be in equilibrium?

The forces must balance in both directions independently, so that the total force each way is matched in each of the two directions separately. Balancing in one direction alone is not enough: a resultant left over in the other direction would still make the particle accelerate.

Several forces on a particle in equilibrium are drawn nose to tail. What shape do they form, and why?

They form a closed polygon , ending exactly where the first arrow began. Drawing forces nose to tail builds up their resultant, and in equilibrium that resultant is zero, so the chain of arrows has to return to its starting point.

True or False? For a block on a slope you may work parallel and perpendicular to the slope rather than horizontally and vertically.

True. Any pair of perpendicular directions will do, and on a slope, parallel and perpendicular to the surface is usually far less work. The normal reaction then lies along one of the two directions and any friction along the other, so neither has to be broken into components.

You have written two equilibrium equations, one for each direction. Why might one of them be much easier to start with?

Because one direction often has fewer unknown forces in it, so its equation may contain only one unknown and can be solved on its own. That value then goes into the other equation, turning a pair of equations into two quick steps rather than a simultaneous solve.

ASMathsCambridge (CIE)MechanicsFlashcardsForces & EquilibriumForces

Forces (Cambridge (CIE) AS Maths: Mechanics): Flashcards

Exam code: 9709

1/19

0Still learning

Know0

FrontForce Diagrams
Define force diagram.

Was this flashcard helpful?

Cards in this collection (19)

Define force diagram.
A force diagram is a sketch of a situation showing every force acting on each particle, each drawn as an arrow pointing the way that force acts.
The magnitude of each force is written beside its own arrow, in newtons.
Fill in the letter normally used on a force diagram for each of these forces:
tension $______$ , friction $______$ , normal reaction $______$
tension T, friction F, normal reaction R
Weight uses W, and thrust also uses T, so a $T$ on a diagram may be either a pull or a push and the arrow is what tells you which.
Why must a force diagram often show forces that the question never mentions?
Because the diagram has to show every force acting on the particle, not only the ones the question happens to name.
An object with mass always has a weight, and an object resting on a surface always has a normal reaction, so both belong on the diagram whether or not the question refers to them.
A block on a slope is connected over a pulley to a hanging mass. Besides the forces, what else should the diagram show?
The direction of the acceleration of each object, marked with its own arrow.
The two arrows point different ways, since one object descends while the other rises, and marking them settles which direction counts as positive in each equation of motion.
True or False?
On a force diagram for a block on a slope, the weight arrow is drawn perpendicular to the slope.
False.
The weight acts vertically downwards whatever the surface is doing, so on a slope its arrow is not perpendicular to the plane.
It is the normal reaction that is perpendicular to the slope, so the two arrows sit at an angle to each other rather than in line.
In a connected system, why must you be careful about which particle each force acts on?
Because an equation of motion describes one particle at a time, and it may contain only the forces acting on that particle.
The tension in a connecting string acts on both, but the weight of one object acts on that object alone, so putting it into the other's equation would be wrong.
Define resultant force.
The resultant force is the sum of all the forces acting on a particle.
It is the single force that would have exactly the same effect as all of those forces combined.
State Newton's first law of motion.
An object at rest stays at rest, and an object moving with constant velocity keeps moving with constant velocity, unless an unbalanced force acts on it.
An unbalanced force is one that is not cancelled by another force in the opposite direction, so it leaves a resultant force that is not zero, and the object accelerates.
Define equilibrium, for a particle.
A particle is in equilibrium when the resultant force acting on it, the sum of all the forces, is zero.
Every force is then cancelled by others, so the particle does not accelerate.
True or False?
Forces on a particle can only balance if the same number of forces act in each direction.
False.
What matters is the total force in each direction, not how many forces there are.
For example, forces of $7 N$ and $5 N$ acting to the right are balanced by a single force of $12 N$ acting to the left.
The resultant force on a particle is zero. What can you say about how it is moving?
The particle is either at rest or moving with constant velocity.
A zero resultant force does not mean the particle is stationary. It means the particle is not accelerating, so whatever it was doing, it carries on doing.
A sign hangs at rest, held up by two strings. Complete the equation used to find an unknown force:
total $______$ force = total $______$ force
total upward force = total downward force
For the sign, the two tensions added together equal its weight.
Define coplanar forces.
Coplanar forces are forces that all lie in the same plane, so the whole situation can be drawn on one flat diagram.
Working in two dimensions means working with coplanar forces.
What must be true of the two directions you resolve in?
They must be perpendicular to each other.
A force lying along one of them then has no effect along the other, which is what lets the two directions be treated as two separate one-dimensional problems.
A particle in a plane has several forces acting on it. What has to be true in each of your two directions for it to be in equilibrium?
The forces must balance in both directions independently, so that the total force each way is matched in each of the two directions separately.
Balancing in one direction alone is not enough: a resultant left over in the other direction would still make the particle accelerate.
A particle of mass $2 kg$ is in equilibrium under forces of $(x + 7) N$ to the left, $(4 x + 2) N$ upwards and $F N$ to the right, together with its own weight. Taking $g = 10 {m s}^{- 2}$ , find $x$ .
The only vertical forces are the $(4 x + 2) N$ force and the weight, which is $2 \times 10 = 20 N$ downwards.
Balancing them gives $4 x + 2 = 20$ , so $4 x = 18$ and $x = 4.5$ .
Several forces on a particle in equilibrium are drawn nose to tail. What shape do they form, and why?
They form a closed polygon, ending exactly where the first arrow began.
Drawing forces nose to tail builds up their resultant, and in equilibrium that resultant is zero, so the chain of arrows has to return to its starting point.
True or False?
For a block on a slope you may work parallel and perpendicular to the slope rather than horizontally and vertically.
True.
Any pair of perpendicular directions will do, and on a slope, parallel and perpendicular to the surface is usually far less work.
The normal reaction then lies along one of the two directions and any friction along the other, so neither has to be broken into components.
You have written two equilibrium equations, one for each direction. Why might one of them be much easier to start with?
Because one direction often has fewer unknown forces in it, so its equation may contain only one unknown and can be solved on its own.
That value then goes into the other equation, turning a pair of equations into two quick steps rather than a simultaneous solve.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Constant AccelerationNext:Newton's Second Law